A mobile is formed by supporting four metal butterflies of equal mass m from a string of length L. The points of support are evenly spaced a distance l apart as shown in Figure P5.54. The string forms an angle 0, with the ceiling at each endpoint. The center section of string is horizon- tal. (a) Find the tension in each section of string in terms of 0,, m, and g. (b) In terms of 0,, find the angle 0, that the sections of string between the outside butterflies and the inside butterflies form with the horizontal. (c) Show that the distance D between the endpoints of the string is L D = 2 cos 0, + 2 cos[un "( an 0,] + 1 co[an (} tan 0,] + 1 D 0, m L = 5€ m m m Figure P5.54

A mobile is formed by supporting four metal butterflies of equal mass m from a string of length L. The points of support are evenly spaced a distance l apart as shown in Figure P5.54. The string forms an angle 0, with the ceiling at each endpoint. The center section of string is horizon- tal. (a) Find the tension in each section of string in terms of 0,, m, and g. (b) In terms of 0,, find the angle 0, that the sections of string between the outside butterflies and the inside butterflies form with the horizontal. (c) Show that the distance D between the endpoints of the string is L D = 2 cos 0, + 2 cos[un "( an 0,] + 1 co[an (} tan 0,] + 1 D 0, m L = 5€ m m m Figure P5.54

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Related questions

Q: frictionless pulley at the top of the inclines as shown, so the blocks can slide together. The mass…

Q: A 4.00 kg block sits on a table top with a coefficient of static friction of 0.470 and a coefficient…

A: Given,

Q: A block is lying on an inclined plane that makes an angle of 20 degrees with the horizontal. What…

Q: Two blocks are positioned on surfaces, each inclined at the same angle of 51.2 degrees with respect…

A: Given: θ=51.2°μ=0.60mass of black block m1=6.22 kgmass of white block m2=?a1=a2=1.5 m/s2

Q: A large, 20,000-kg flatbed truck is carrying a 10,000-kg load of steel beams, and the driver has…

Q: A toy car is held at the top of a ramp and is released. Is it possible with an unknown friction…

Q: A box on a rough floor is pulled with a force of 1000N along a rope that creates an angel 25° above…

A: Given data: Magnitude of pulling force is, F=1000 N. Angle made from horizon is, θ=25∘. Coefficient…

Q: Two blocks are positioned on surfaces, each inclined at the same angle of 54.9 degrees with respect…

Q: A 128 kg crate is sitting at the top of a ramp, which is inclined at an angle of 34 degrees with…

Q: Two blocks are positioned on surfaces, each inclined at the same angle of 47.2 degrees with respect…

A: Given that:- Mass of black block=5.82kg

Q: Two blocks are positioned on surfaces, each inclined at the same angle of 52.5 degrees with respect…

Q: (b) What are the drag forces in newtons at 79 km/h and at 105 km/h for a Hummer H2? (Drag area =…

A: b) Conversion 79 kmh=79 km/h0.277778 mskm/h=21.9444 ms105 kmh=105 km/h0.277778 mskm/h=29.1667 ms The…

Q: In the figure, the block of mass m is at rest on an inclined plane that makes an angle θ with the…

A: Given: The mass of the object is m. The angle of the inclination is θ. The system is in equilibrium.…

Q: A M1 =1000-kg car is on a rough ramp that is inclined at θ = 20° above the horizontal. It is…

Q: Two blocks are positioned on surfaces, each inclined at the same angle of 58.7 degrees with respect…

A: Block moves with constant velocity, it means acceleration of the block is zero or there is balance…

Q: Two blocks are positioned on surfaces, each inclined at the same angle of 54.8 degrees with respect…

A: Given: The angle is θ=54.8°. The mass of the black block is m1=3.64 kg. The coefficient of kinetic…

Q: Suppose the ski patrol raises a rescue sled and victim, having a total mass of 85.0 kg, up a ? =…

Q: Two blocks are positioned on surfaces, each inclined at the same angle of 41.8 degrees with respect…

Q: Jane needs to swing across a river filled with man-eating crocodiles in order to rescue Tarzan from…

Q: Two blocks are positioned on surfaces, each inclined at the same angle of 49.9 degrees with respect…

A: Draw the free-body diagram of the black block.

Q: Do it asap if possible

A: Given that,Mass : m = 81 (kg)A rectangular box with dimension : 24×47×170 cmThe density : ρ = 1.2…

Q: Two blocks are positioned on surfaces, each inclined at the same angle of 48.8 degrees with respect…

A: Given:- Two blocks are positioned on surfaces, each inclined at the same angle of θ=48.8o The mass…

Q: A 81 kg skydiver can be modeled as a rectangular "box" with dimensions 24 cm × 47 cm × 170 cm. If he…

A: Given that,Mass : m = 81 (kg)A rectangular box with dimension : 24×47×170 cmThe density : ρ = 1.2…

Q: A 4000-kg car is being towed up a smooth frictionless incline ramp inside a truck by chains at a…

A: Given data:- The mass of the car is M = 4000 kg. The angle made by the ramp is θ = 53o. The angle…

Q: Two blocks are positioned on surfaces, each incline at the same angle of 59.8° with respect to the…

A: Although the figure of the question is missing But since all the data given for both the blocks is…

Q: Two blocks are positioned on surfaces, each inclined at the same angle of 40.6 degrees with respect…

A: Given Data:- Mass of the black block is mb = 2.77 kg Angle of inclination is, θ = 40.60 Coefficient…

Q: force exerted by the kneecap on the upper leg bone (the femur). XN X (counter-clockwise from an axis…

Q: blocks can slide together. The mass of the black block is 7.87 kg, and the coefficient of kinetic…

Q: 60.0-kg box is dragged up a 20º incline by a rope held 35º above the horizontal. The coefficient of…

Q: Two blocks are positioned on surfaces, each inclined at the same angle of 54.4 degrees with respect…

A: Angle of inclination Mass of black block Coefficient of kinetic friction Acceleration due to…

Q: : Fig. 2(a) shows three crates being pushed on a frictionless floor by a force F. A force of modulus…

Q: Two blocks are positioned on surfaces, each inclined at the same angle of 44.3 degrees with respect…

Q: Two blocks are positioned on surfaces, each inclined at the same angle of 57.9 degrees with respect…

Q: Two blocks are positioned on surfaces, each inclined at the same angle of 50.5 degrees with respect…

Q: wo blocks are positioned on surfaces, each inclined at the same angle of 52.3 degrees with respect…

A: Newton's Second Law of Motion According to Newton's Second Law of motion, the rate of change of…

Q: A 300kg piano is at rest on a ramp with an angle of inclination of 27°. The angle is such that the…

Q: A 100-N box rest on top of 45° inclined plane. The box is connected to a hanging object of unknown…

A: Given:- The Weigh of the box is m1g = 100 N it on the rest position on the top of the 45°…

Q: Right before a shoe starts sliding down an iclined ramp, θ reaches a maximum which means the force…

A: We need to explain why the object remains stationary in the given condition.

Q: Two blocks are positioned on surfaces, each inclined at the same angle of 55.4 degrees with respect…

A: mb=7.71 kgμ=0.600 θ=55.4mw=?v=constanta=0T=tension in ropeg= gravitational acc.g=9.8 ms2N=normal…

Q: A mobile is formed by supporting four metal butterflies of equal mass m from a stringof length L.…

A: The mass of metal butterflies is m, the length of the string is L, the distance of the point of…

Q: The forces on an aircraft flying at altitude are shown in the picture. An F35 fighter jet has a mass…

A: Given: Mass of fighter jet: m=14000 [kg] Thrust force: Tmax=190000 [N] Force of air drag: Fa=40000…

Q: A 25.0 kg box of textbooks rests on a loading ramp that makes an angle αα with the horizontal. The…

Q: A Valentine’s day decoration with the mass of 5 kg hang from two lightweight cables, one on each…

A: Assume tension in cable is T. The tension has two component horizontal and vertical component. The…

Q: Two blocks are positioned on surfaces, each inclined at the same angle of 55.4 degrees with respect…

Q: A Smart Fortwo® car has a mass of 730 kg, which we assume on a flat surface is evenly distributed…

A: We are given mass of car. We are also given the 4 tires and the coefficient of friction. The mass is…

Q: A block weighing 60.0 N rests on a plane inclined at 25.0° to the horizontal. A force F is applied…

A: Given, Weight of Block = 60 N Angle with plane inclined with horizontal = 250 Angle of applied…

Question

A mobile is formed by supporting four metal butterflies
of equal mass m from a string of length L. The points of
support are evenly spaced a distance l apart as shown in
Figure P5.54. The string forms an angle 0, with the ceiling
at each endpoint. The center section of string is horizon-
tal. (a) Find the tension in each section of string in terms
of 0,, m, and g. (b) In terms of 0,, find the angle 0, that the
sections of string between the outside butterflies and the
inside butterflies form with the horizontal. (c) Show that
the distance D between the endpoints of the string is
L
D =
2 cos 0, + 2 cos[un "( an 0,] + 1
co[an (} tan 0,] + 1
D
0,
m
L = 5€
m
m
m
Figure P5.54

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Part (a)

Step 2

Step 3

Step 4

Step 5

Part (b)

Step 7

Part (c)

Step 9

Step 10

Trending now

This is a popular solution!

Step by step

Solved in 10 steps with 15 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

A rope one meter long rests on a table where the coefficient of friction is 0.50. What maximum length of rope can hang over the side before the whole rope will slip off?
A constant force Fa pushes a 22.5-kg box across a rough horizontal surface. The magnitude of Fa is 185 N and the force is inclined at an angle of θ = 30.0° below the horizontal. The coefficient of kinetic friction between the box and the surface is μk = 0.500. What is the magnitude of the box's acceleration?
A 127 log crate is sitting at the top of a ramp, which is inclined at an angle of 39 degrees with respect to the horizontal. What is the magnitude and the normal force in Newtons acting on the box?
A traffic light weighing 122 N hangs from a cable tied to two other cables fastened to a support as in Figure 5.10a. cables make angles of 0, 37.0° and 0, The upper = 53.0° with the horizontal. These upper cables are not as %3D %3D strong as the vertical cable and will break if the tension in them exceeds 100 N. Does the traffic light remain hanging in this situation, or will one of the cables break?
Two blocks are positioned on surfaces, each inclined at the same angle of 45.1 degrees with respect to the horizontal. The blocks are connected by a rope which rests on a frictionless pulley at the top of the inclines as shown, so the blocks can slide together. The mass of the black block is 7.86 kg, and the coefficient of kinetic friction for both blocks and inclines is 0.540. Assume static friction has been overcome and that everything can slide. What is must be the mass of the white block if both blocks are to slide to the LEFT at a constant velocity? 17.02 kg 2.36 kg 26.17 kg 7.86 kg
A 34.3 kg child is sitting at the top of a slide, which is inclined at an angle of 40 degrees with respect to the horizontal. What is the minimum value for the coefficient of static friction that allows the child to stay at rest at the top of the slide?
A 104 kg crate is sitting at the top of a ramp, which is inclined at an angle of 28 degrees with respect to the horizontal. What is the minimum value for the coefficient of static friction that allows the box to stay at rest at the top of the ramp?
Two blocks are positioned on surfaces, each inclined at the same angle of 52.4 degrees with respect to the horizontal. The blocks are connected by a rope which rests on a frictionless pulley at the top of the inclines as shown, so the blocks can slide together. The mass of the black block is 5.40 kg, and the coefficient of kinetic friction for both blocks and inclines is 0.350. Assume static friction has been overcome and that everything can slide. What is must be the mass of the white block if both blocks are to slide to the RIGHT at an acceleration of 1.5 m/s^2? 1.98 kg 2.55 kg 4.61 kg 2.07 kg
The figure below shows a box with a mass of m= 3.90 kg on a ramp inclined at an angle of 35.0°. The coefficient of static friction between the box and the ramp is 0.250. Find the minimum magnitude of the force F (in N), applied to the box in a direction perpendicular to the ramp, that will prevent the box from sliding down the ramp. N m 35.0°
a 12.0 kg box is sitting motionless on a plane, which is tilted to an angle of 30 degrees. what must the minimum value of the coefficient of static friction between the box and the surface of the plane be, so that the box does not move? include a system diagram and a FBD in your solution,
Two blocks are positioned on surfaces, each inclined at the same angle of 54.5 degrees with respect to the horizontal. The blocks are connected by a rope which rests on a frictionless pulley at the top of the inclines as shown, so the blocks can slide together. The mass of the black block is 7.57 kg, and the coefficient of kinetic friction for both blocks and inclines is 0.360. Assume static friction has been overcome and that everything can slide. What is must be the mass of the white block if both blocks are to slide to the LEFT at a constant velocity?
Two blocks are positioned on surfaces, each inclined at the same angle of 42.2 degrees with respect to the horizontal. The blocks are connected by a rope which rests on a frictionless pulley at the top of the inclines as shown, so the blocks can slide together. The mass of the black block is 6.63 kg, and the coefficient of kinetic friction for both blocks and inclines is 0.550. Assume static friction has been overcome and that everything can slide. What is must be the mass of the white block if both blocks are to slide to the RIGHT at a constant velocity?